master-of-science (m.sc.) physics - uni-freiburg.de

Handbook of Modules

Master-of-Science (M.Sc.) Physics

Physikalisches Institut Fakultät für Mathematik und Physik Albert-Ludwigs-Universität Freiburg

Fach Physik / Physics

Abschluss Master of Science (M.Sc.)

Prüfungsordnungsver-sion 2015

Art des Studiengangs konsekutiv

Studienform Vollzeit

Regelstudienzeit 4 Semester

Studienbeginn Winter- und Sommersemester

Hochschule Albert-Ludwigs-Universität Freiburg

Fakultät Fakultät für Mathematik und Physik

Institut Physikalisches Institut

Homepage www.physik.uni-freiburg.de

Profil des Studiengangs

In the first year participants consolidate their knowledge in advanced theoretical and experimental physics covering state-of-the-art topics in the institute's core research areas Atomic, Molecular and Optical Sciences, Condensed Matter and Applied Physics, and Particles, Fields and Cosmos. Advanced quantum me-chanics and the Master Laboratory are mandatory classes. Advanced physics courses can be selected from a range of state-of-the-art topics in the main re-search areas of the department. During their final one-year Master thesis, stu-dents specialize in a particular field by participating in a cutting-edge research project at the Institute of Physics or one of the associated research centers.

Ausbildungsziele/ Qualifikationsziele des Studiengangs

The Master programme aims to continue, deepen and broaden studies begun at Bachelor level. It provides a comprehensive scientific education in advanced theoretical and experimental physics. Successful students are qualified for in-dependent research in physics and will be prepared for a scientific career in research, academia, or industry. Furthermore, they are on the next step towards a PhD study, which generally is a prerequisite for leading positions in economy or industry, or for a later academic career.

Sprache Englisch

Zugangs- voraussetzungen

Qualifizierter Bachelor-Abschluss in Physik oder einem gleichwertigen Studiengang. Außerdem:

• mindestens 32 ECTS-Punkte in Theoretischer Physik, • mindestens 32 ECTS-Punkte in Experimenteller Physik, • mindestens 24 ECTS-Punkte in Mathematik, • mindestens 18 ECTS-Punkte aus physikalischen Praktika, • Bachelor-Arbeit in Physik (10 ECTS-Punkte), • Niveau B2 in Englisch.

Preliminary notes:

The handbook of modules does not substitute the course catalogue, which is updated every se-mester to provide variable information about the courses (e.g. time and location).

List of Abbreviations M.Sc. Master of Science Credit hrs A credit hour corresponds to a course of a duration of 45 minutes per week

(in German: Semesterwochenstunden, SWS) SL Assessed coursework („Studienleistung“), ungraded, does not contribute to final grade PL Exam („Prüfungsleistung“), graded, contributes to final grade L Lecture E Exercise/Tutorials S Seminar Lab Laboratory SoSe Summer semester (summer term) WiSe Winter semester (winter term) ECTS Credit Points based on the European Credit Transfer System (ECTS-Points)

Version: 01.04.2021 University Freiburg

Handbook of Modules - M.Sc. Physics

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Table of Contents

1. Master-of-Science (M.Sc.) in Physics ...................................................................... 4

1.1. Programme Structure ...................................................................................................... 4

1.2. Forms of Assessment (Studienleistung SL, Prüfungsleistung PL) ................................... 4

1.3. Workload / ECTS-Point System ...................................................................................... 5

1.4. Contents of Modules ....................................................................................................... 5

1.5. Determination of final grade ............................................................................................ 6

2. Organisation of studies ............................................................................................ 7

2.1. Study plan ....................................................................................................................... 7

2.2. Enrolment for lectures and courses ................................................................................. 7

2.3. Registration for exams (SL or PL) ................................................................................... 8

2.4. Retaking exams .............................................................................................................. 8

3. List of Modules and Description .............................................................................. 9

3.1. Advanced Quantum Mechanics (10 ECTS credit points) ................................................. 9

3.2. Advanced Physics 1 (9 ECTS credit points) .................................................................. 11



3.5. Elective Subjects (9 ECTS credit points) ....................................................................... 15

3.6. Term Paper (6 ECTS credit points) ............................................................................... 16

3.7. Master Laboratory (8 ECTS credit points) ..................................................................... 17

3.8. Research Traineeship (30 ECTS credit points) ............................................................. 19

3.9. Master Thesis (30 ECTS credit points) .......................................................................... 20

4. Advanced Physics Lectures ................................................................................... 21

4.1. Advanced Atomic and Molecular Physics ...................................................................... 21

4.2. Advanced Optics and Lasers ........................................................................................ 22

4.3. Condensed Matter I: Solid State Physics ...................................................................... 23

4.4. Condensed Matter II: Interfaces and Nanostructures .................................................... 24

4.5. Advanced Particle Physics ............................................................................................ 25



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4.6. Particle Detectors .......................................................................................................... 27

4.7. Hadron Collider Physics ................................................................................................ 28

4.8. Astroparticle Physics ..................................................................................................... 30

4.9. Theoretical Condensed Matter Physics ......................................................................... 31

4.10. Classical Complex Systems ........................................................................................ 32

4.11. Complex Quantum Systems ....................................................................................... 34

4.12. Quantum Field Theory ................................................................................................ 36

4.13. General Relativity ....................................................................................................... 37

4.14. Quantum Optics .......................................................................................................... 39

4.15. Quantum Chromodynamics ........................................................................................ 40

4.16. Computational Physics: Materials Science.................................................................. 41

5. Elective Subjects ..................................................................................................... 43

5.1. Microscopy and Optical Image Formation (7 ECTS) ..................................................... 43

5.2. Biophysik - Grundlagen und Konzepte / Biophysics - Basics and concepts (7 ECTS) ... 45

5.3. Nano-Photonics - Optical manipulation and particle dynamics (7 ECTS)....................... 47

5.4. Wave Optics (7 ECTS) .................................................................................................. 49

5.5. Laser-based Spectroscopy and Analytical Methods (5 ECTS) ...................................... 52

5.6. Photovoltaic Energy Conversion (5 ECTS) .................................................................... 54

5.7. Multi-junction solar cell technology and concentrator photovoltaic (3 ECTS) ................. 55

5.8. Solar Physics (5 ECTS) ................................................................................................ 56

5.9. Modern Astronomical Instrumentation (5 ECTS) ........................................................... 57

5.10. Dynamic Systems in Biology (7 ECTS) ....................................................................... 58

5.11. Molecular Dynamics & Spectroscopy (7 ECTS) .......................................................... 59

5.12. Physics of Nano-Biosystems (5 ECTS) ....................................................................... 60

5.13. Physics of Medical Imaging Methods (5 ECTS) .......................................................... 61

5.14. Biophysics of Cardiac Function and Signals (5 ECTS) ................................................ 63

5.15. Computational Neuroscience: Models of Neurons and Networks (7 ECTS) ............... 64

5.16. Computational Neuroscience: Simulation of Biological Neuronal Networks (5 ECTS) . 66

5.17. Experimental Polymer Physics (9 ECTS) .................................................................... 67

5.18. Physical Processes of Self-Assembly and Pattern Formation (7 ECTS) .................... 68

5.19. Fundamentals of Semiconductors & Optoelectronics (5 ECTS) .................................. 70



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5.20. Semiconductor Devices (5 ECTS) .............................................................................. 71

5.21. Theory and Modeling of Materials (5 ECTS) ............................................................... 72

5.22. Quantum Transport (7 ECTS) ..................................................................................... 73

5.23. Low Temperature Physics (9 ECTS) ........................................................................... 74

5.24. Statistics and Numerics (7 ECTS) ............................................................................... 76

5.25. Computational Physics: Density Functional Theory (7 ECTS) ..................................... 77

6. Example study plans for optional specialisation ................................................. 78



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1. Master-of-Science (M.Sc.) in Physics

1.1. Programme Structure

The Physics Institute offers a research-oriented curriculum leading to a Master of Science degree in Physics. The programme comprises a total of 120 ECTS credit points (CP), which are collected in various compulsory and elective modules as defined by the study regulations. The programme comprises the following modules and courses:

Module Type Contact hours ECTS

Compul-sory/

Elective

Recom-mended semester

Assessment

Advanced Quantum Mechanics L+E 4+3 10 C 1 or 2 SL: exercises

PL: written exam

Advanced Physics 1 L+E 4+2 9 E 1 or 2 SL: exercises PL: written or oral exam

Advanced Physics 2 L+E 4+2 9 E 1 or 2 SL: exercises PL: written or oral exam

Advanced Physics 3 L+E 4+2 9 E 1 or 2 SL: exercises SL: written or oral exam

Elective Subjects varia-ble variable 9 E 1 or 2 SL: exercises and/or

written or oral exam

Term Paper S 2 6 E 1 or 2 PL: presentation and written report

Master Laboratory Lab 10 8 C 1 or 2 PL: oral exam, practical achievement, written report, presentation

Research Traineeship - - 30 C 3 SL: internship

Master Thesis - - 28 2 C 4 PL: thesis

SL: presentation Abbreviations in table: Type = type of course; L = lecture; E = exercises; S = seminar; Lab = laboratory; C = compulsory module; E = elective module; SL = assessed coursework (´Studienleistung´); PL = exam (‘Prüfungsleistung’)

1.2. Forms of Assessment (Studienleistung SL, Prüfungsleistung PL)

A module is successfully passed, when all corresponding assessments have been accomplished. The following forms of assessments are distinguished:

Studienleistungen (SL) are individual achievements, which are accomplished in combination with a corresponding course or lecture. In general, SLs consist of the successful participation in written exercises or exams. In exercises, which rely on the interaction between students and lec-turers or tutors, passing a SL requires also the regular attendance and active participation in the exercise classes. Details on the SL will be announced by the lecturer in the beginning of the se-mester. SLs are not marked (non-graded) and therefore do not contribute to the final mark. Prüfungsleistungen (PL) are written or oral module exams, which test all components of a mod-ule. PLs are marked (graded) and contribute to the final mark of the degree according to the weight listed in 1.5.



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1.3. Workload / ECTS-Point System

The European Credit Transfer and Accumulation System (ECTS) is a standard for comparing the study attainment and performance of students of higher education across the European Union and other collaborating European countries. It provides more compatibility and mobility between the programmes at different institutions and different countries.

The ECTS credit points (CP), which can be acquired, determine the time requirements for a mod-ule with one CP corresponding to a workload of about 30 hours. This workload includes partici-pation in courses, preparation and post-processing of the courses, exercises and exams. The ECTS-System enables the accumulation of credits and marks throughout the entire studies and facilitates documenting the study progress.

1.4. Contents of Modules

Within the Master’s programme some modules are compulsory and others offer the possibility to select courses at the student’s own choice.

Advanced Quantum Mechanics (10 ECTS credit points) All students have to accomplish the compulsory module Advanced Quantum Mechanics. The module mark is the mark of the final exam (PL).

Advanced Physics 1 (9 ECTS credit points) Within the module Advanced Physics 1 students may select an lecture on Advanced Experimental or Advanced Theoretical Physics by their own choice. Eligible lectures are listed in section 4 and in the course catalogue for the current semester. The module mark is the mark of the final exam (PL).

Advanced Physics 2 (9 ECTS credit points) Within the module Advanced Physics 1 students may select an lecture on Advanced Experimental or Advanced Theoretical Physics by their own choice. Eligible lectures are listed in section 4 and in the course catalogue for the current semester. The module mark is the mark of the final exam (PL).

Advanced Physics 3 (9 ECTS credit points) Within the module Advanced Physics 1 students may select an lecture on Advanced Experimental or Advanced Theoretical Physics by their own choice. Eligible lectures are listed in section 4 and in the course catalogue for the current semester. If both lectures in Advanced Physics 1 and 2 are from the same field (Experimental/Theoretical Physics) a lecture from the other field has to be selected. The module is an unmarked course achievement (SL).

Elective Subjects (9 ECTS credit points) All 9 ECTS credits of this module can be acquired by selecting different courses by own choice. The selected courses have to be at the Master’s level, i.e. from the M.Sc. programme in Applied Physics and/or other Master programmes. The examination committee may permit other courses on request. Note that for courses at other faculties different application modalities and requirements may ap-ply. Students are responsible to proof successful participation, so that the credits can be booked by the examination office of physics.



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Term Paper (6 ECTS credit points) Within the elective module Term Paper students select a seminar on a specific topic, with several seminars offered each term.

Master Laboratory (8 ECTS credit points) In the Master Laboratory students accomplish different lab experiments with the total workload of 8 ECTS credit points. Successful completion of the Master Laboratory is prerequisite for beginning the Research Traineeship.

Research Traineeship (30 ECTS credit points) Before working on their Master Thesis students engage in a Research Traineeship, which is ac-complished in a six-month period. The aim of this module is to acquire preliminary knowledge in a certain research topic in preparation for the Master Thesis. For their traineeship and thesis stu-dents select a supervisor at the Institute of Physics or the associated research institutes. Admission to the Master Research module requires successful accomplishment of the module Master Labor-atory and three of the four marked courses in the modules Advanced Quantum Mechanics, Ad-vanced Physics 1, 2, and Term Paper.

Master Thesis (30 ECTS credit points) In the final six-months master thesis students perform independent research on a specialized topic in applied physics and prepare a written thesis. Typically, the Master Thesis is accomplished at the same research group as the traineeship. In a period of 2 weeks before to 4 weeks after submit-ting the Master Thesis, the students present the results of their thesis work in a public presentation.

1.5. Determination of final grade

The individual module marks contribute to the final grade with the following weights:

Module weight

Advanced Quantum Mechanics 11 %

Advanced Physics 1 11 %

Advanced Physics 2 11 %

Term Paper 7 %

Master Laboratory 10 %

Master Thesis 50 %



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2. Organisation of studies

2.1. Study plan

In the first year, the master students consolidate their knowledge in compulsory and elective courses. For the first and second semester, an equally balanced workload is recommended with a total of about 30 ECTS credit points each.

The following study plan is recommended for students starting their studies in the winter semester:

FS Module ∑ ECTS

1 Advanced Quantum Mechanics 10 ECTS

Advanced Physics 1 9 ECTS Term Paper

6 ECTS Master La-boratory 8 ECTS

33

2

Advanced Physics 2 9 ECTS

Elective Subjects Advanced Physics and/or other discipline by own choice 9 ECTS

27 Advanced Physics 3 9 ECTS

3 Research Traineeship 30 ECTS 30

4 Master Thesis (Thesis and Presentation) 30 ECTS 30

Note that, Advanced Quantum Mechanics is only offered in the winter term, so dependent on the start of the Master studies (start in winter or summer semester) the course can be taken either in the first or second semester. The Master Laboratory is offered as a block course during the semes-ter break following the winter term. Dependent on the start of studies, students participate either in the first or second semester.

2.2. Enrolment for lectures and courses

It is possible to enrol for lectures and courses in the online Campus System. Note that for partici-pation in lectures, a registration is not mandatory but recommended. Registration is possible via the electronic campus management system HISinOne www.uni-freiburg.de/go/campus. In order to take part in the final exam a separate registration is required (see 2.3). For participation in the master laboratory students have to register directly at the head of the lab course, e.g. via the central learning platform ILIAS https://ilias.uni-freiburg.de. Details see on www.physik.uni-freiburg.de/studium/labore).

http://www.uni-freiburg.de/go/campus

https://ilias.uni-freiburg.ded/



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2.3. Registration for exams (SL or PL)

In order to finish a module all contained exercises and exams (Studienleistungen SL and Prüfungs-leistungen PL) have to be passed. For participating in the exams a registration in due time via the electronic campus management system HISinOne www.uni-freiburg.de/go/campus is necessary. The common registration period is typically starting with the beginning of the semester end ends one week before the first exam. Within this period registration to and deregistration from an exam is possible. The exact registration period for each semester and other modalities can be found on the webpage of the examination office www.physik.uni-freiburg.de/studium/pruefungen.

2.4. Retaking exams

Failed examinations may be retaken twice in the modules Advanced Quantum Mechanics and Ad-vanced Physics 1 and 2, and once in the modules Term Paper, Master Laboratory, and Master Thesis. It is not permitted to retake examinations to improve the marks.

http://www.uni-freiburg.de/go/campus

http://www.physik.uni-freiburg.de/studium/pruefungen



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3. List of Modules and Description

3.1. Advanced Quantum Mechanics (10 ECTS credit points)

Module 07LE33M-AQM

Advanced Quantum Mechanics 10 ECTS

Responsibility Dean of Studies, Lecturers for Theoretical Physics

Courses Type Credit hrs

ECTS Assessment Term

Advanced Quantum Mechanics

L 4 10 PL: written exam WiSe


E 3 SL: exercises WiSe

Total: 4+3 10

Required academic assessment

The final module exam (PL) is a written exam. The course achievement (SL) is the regular and successful participation in the exercises. Students have to register online for the exercises and for the final exam according to the regulations of the examination office.

Grading The final grade of the module is the grade of the final exam.

Qualification objectives

• Students know the foundations of scattering theory and are able to apply these to problems involving simple potentials.

• Students know the representations of the rotational group and their relevance for quantum theory. They have a fundamental knowledge in group theory and repre-sentation theory in general. They know the meaning of product representations and irreducible representations. They are able to apply Clebsch-Gordon coeffi-cients to simple problems involving angular momentum and spin in atomic spectra.

• Students know the connection between spin and statistics. They are able to sym-metrize respectively anti-symmetrize multi-particle states. They can describe the methods of Hartree- and Hartree-Fock and apply them to simple multi-particle sys-tems.

• Students know the fundamentals of time-dependent perturbation theory and can apply it to specific time-dependent problems.

• Students know Dirac’s equation and can solve it for the free case.

Course content • Scattering theory: scattering amplitude and cross-section, partial wave expansion, Lippmann-Schwinger equation and Born series.

• Fundamentals of the representation theory of groups, in particular of the rotation group SO(3). Tensor product representations and irreducible representations. Wigner-Eckart theorem. Applications to angular momentum and spin couplings in atomic, molecular and condensed matter physics.

• Time-dependent perturbation theory: Dyson-expansion, Fermi’s Golden Rule, ex-amples of application to important time-dependent quantum processes.



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• Many-particle systems: identical particles, spin-statistic theorem, variational prin-ciples, Hartree and Hartree-Fock approximations.

• Interaction between radiation and matter. Quantization of the electromagnetic field. Interaction Hamiltonian, emission and absorption.

• Relativistic quantum mechanics and quantum field theory; Dirac equation, quanti-zation of Klein-Gordon and Dirac’s equation.

Workload (hours)

Course Type Contact hrs Self-studies Total


L 60 h 120 h 180 h


E 45 h 75 h 120 h

Total: 105 h 195 h 300 h

Usability M.Sc. Physics, M.Sc. Applied Physics

Previous knowledge Contents of lectures Theoretical Physics I-IV (B.Sc. Physics)

Language English



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3.2. Advanced Physics 1 (9 ECTS credit points)

Module 07LE33K-ADV_PHYS1


Responsibility Dean of Studies, Lecturers of the Institute of Physics


ECTS Assess-ment

Term

Advanced Physics L 4 9 PL: written or oral exam

WiSe + SoSe

Advanced Physics E 2 SL: exercises

WiSe + SoSe

Total: 4+2 9


The final module exam (PL) is a written exam. The course achievement (SL) is the regular and successful participation in the exercises. Students have to register online for the exercises and for the final exam according to the regulations of the examination office.



• Students obtain advanced knowledge in particular field of modern physics. • Students are familiar with current problems and research topics in particular fields of

modern research in physics. • Students know advanced tools and methods in particular fields. • Specific qualification objectives for each lecture are listed in individual course de-

scriptions section 4.

Course content A suitable lecture has to be selected by own choice from the list of Advanced Experi-mental or Advanced Theoretical Physics lectures given below. List of eligible Advanced Lectures offered regularly: (Exp = Experimental Lectures; Theo = Theory Lectures)

Lecture Course: Term Advanced Atomic and Molecular Physics Exp WiSe Advanced Optics and Lasers Exp SoSe Condensed Matter I: Solid State Physics Exp WiSe Condensed Matter II: Interfaces and Nanostructures Exp SoSe Advanced Particle Physics Exp WiSe Hadron Collider Physics Exp SoSe Particle Detectors Exp WiSe Theoretical Condensed Matter Physics Theo SoSe Classical Complex Systems Computational Physics: Materials Science

Theo Theo

WiSe SoSe

General Relativity Theo WiSe Quantum Field Theory Theo SoSe



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In addition, various lectures on specialized physics topics are offered on an irregular basis and are indicated in the course catalogue as Advanced Physics lectures. List of eligible Advanced Lectures offered irregularly:

Astro Particle Physics Exp Theoretical Quantum Optics Theo Complex Quantum Systems Theo Quantum Chromodynamics Theo

Workload (hours)


Advanced Physics L 60 h 120 h 180 h

Advanced Physics E 30 h 60 h 90 h

Total: 90 h 180 h 270 h

Usability M.Sc. Physics

Previous knowledge Basic experimental or theoretical physics lecture in the respective field

Language English



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Responsibility Dean of Studies,, Lecturers of the Institute of Physics


ECTS Assess-ment

Term

Advanced Physics L 4 9 PL: written or oral exam

WiSe + SoSe


WiSe + SoSe

Total: 4+2 9


The final module exam (PL) is a written exam. The course achievement (SL) is the regular and successful participation in the exercises. Students have to register online for the exercises and for the final exam according to the announced regulations.




modern research in physics. • Students know advanced tools and methods in particular fields. • Specific qualification objectives for each lecture are listed in individual course de-

scriptions section 4.

Course content A suitable lecture has to be selected by own choice from the catalogue of Advanced Experimental or Advanced Theoretical Physics lectures given in the (online) course catalogue of the Physics Institute. A range of advanced courses is offered on a regular or irregular basis. The specific content of each lecture is detailed in individual course descriptions section 4 or in the online course descriptions.

Workload (hours)




Total: 90 h 180 h 270 h



Language English



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Responsibility Dean of Studies,, Lecturers of the Institute of Physics


ECTS Assess-ment

Term

Advanced Physics L 4 9 SL: written or oral exam

WiSe + SoSe


WiSe + SoSe

Total: 4+2 9


The final module exam (PL) is a written exam. The course achievement (SL) is the regular and successful participation in the exercises. Students have to register online for the exercises and for the final exam according to the regulations.




modern research in physics. • Students know advanced tools and methods in particular fields. • Specific qualification objectives are listed in individual course descriptions..

Course content A suitable lecture has to be selected by own choice from the catalogue of Advanced Experimental or Advanced Theoretical Physics lectures given in the (online) course catalogue of the Physics Institute. A range of advanced courses is offered on a regular or irregular basis. The specific content of each lecture is detailed in individual course descriptions section 4 or in the online course descriptions.If both lectures Advanced Physics 1 and 2 have been selected from one field (Advanced Experimental Phys-ics or Advanced Theory) Advanced Physics 3 has to be chosen from the other field.

Workload (hours)




Total: 90 h 180 h 270 h



Language English



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3.5. Elective Subjects (9 ECTS credit points)

Module 07LE33K-ELSUB

Elective Subjects 9 ECTS

Responsibility Dean of Studies, or Faculty/Department responsible for selected course

Courses Type Credit hrs ECTS Assess-ment

Term

Advanced Physics courses and/or Mathe-matics courses and/or courses by own choice

L+E According to selected courses

9 SL WiSe + SoSe

Total: 9


Subject to selected courses

Grading unmarked


The qualification objects are subject to the selected course.

Course content Students select different courses by own choice in order collect at least 10 ECTS credit points in total. The selection may contain lectures of the M.Sc. Physics program, or of the M.Sc./M.A. programs of other disciplines. The examination committee may admit courses of other external programs upon application. The course content is subject to the selected course. Also lectures of the B.Sc. programme in Mathematics can be chosen with the exception of Analysis I and II, and Linear Algebra I and II. The examination committee may admit courses of other external programmes upon application.

Workload (hours)

Course Contact hrs Self-studies Total

Elective courses subject to selected courses 270 h

Total: 270 h


Previous knowledge Subject to selected courses

Language Subject to selected courses



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3.6. Term Paper (6 ECTS credit points)

Module 07LE33M-TP

Term Paper 6 ECTS

Responsibility Dean of Studies, Lecturers of the Institute of Physics


ECTS Assess-ment

Term

Term paper seminar S 2 6 PL: oral presentation and written

report

WiSe + SoSe

Total: 2 6


Students elaborate and give an oral presentation to a specialized physics topic or an adjacent area and prepare a written documentation. Active participation in all presen-tations of the seminar is expected.

Grading A combined grade is given for the oral presentation and the written documentation.


• Students are able to handle scientific literature and to search in scientific publica-tions

• Students are able to prepare and present a topic of current physical research in front of a broad audience

• Participants have the skills to lead a discussion in a group of students • Students can give scientific lecture and are able to incorporate didactical elements

Course content The research groups of the Institute of Physics offer various seminars each term. Allo-cation and registration to a particular seminar will be in a common event generally held in the first week of the semester. The Term Paper seminar comprises approximately 10 presentations from a coherent field of physics or a neighbouring scientific area.

Workload (hours)


Term paper seminar 21 h 159 h 180 h

Total: 21 h 159 h 240 h

Usability M.Sc. Physics, M.Sc. Applied Physics

Previous knowledge Basic knowledge in respective topic as acquired in self-studies or lecture

Language English



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3.7. Master Laboratory (8 ECTS credit points)

Module 07LE33M-MLAB

Master Laboratory 8 ECTS

Responsibility Head of the master laboratory

Courses Course Type ECTS Assessment Term

Master Laboratory Lab block course

8 PL: experimental work, written report, oral presentation

WiSe

Total: 8

Organisation The Master Laboratory is offered as a block course during the semester break. Students have to register for the course online 10 weeks before the start of the course (https://www.physik.uni-freiburg.de/studium/labore). Students perform 3 experiments and prepare written lab reports. Two experiments have to be completed within one week each. One experiment is performed within an allocated time of two weeks. For this extended experiment the students prepare an oral presen-tation held in a common seminar at the end of the Master Laboratory.


For each experiment the students have to prepare the scientific background, which is tested in an initial written and oral exam, The students perform each experiment in teams of two and prepare written lab report. For one extended experiment the students additionally prepare and give an oral presentation.

Grading For each of the 3 experiments a grade is given based on an initial written and oral exam (test of the preparatory knowledge), the experimental performance and the written re-port (incl. lab report and analysis). In addition, a grade is given for the final oral seminar presentation. All marks contribute equally to the final module grade (arithmetic mean).

Repetition Individual experiments have to be repeated at specially offered dates immediately after the regular end of the laboratory course. In case the entire Laboratory course has to be repeated, this is only possible by participating in the next year’s course is.


• Students are able to perform complex advanced experiments running over several days

• Students are able to apply advanced statistical data analysis methods • Students are able to prepare a written lab report • Students are able to critically evaluate and assess their experimental results

Course content Performance of three Advanced Physics Experiments from Particle & Nuclear Physics, Atomic & Molecular Physics, Solid State Physics and Optics. The current catalogue of laboratory experiments is available online on https://www.physik.uni-freiburg.de/studium/labore/fp/fp2/#section-3

https://www.physik.uni-freiburg.de/studium/labore

https://www.physik.uni-freiburg.de/studium/labore/fp/fp2/#section-3



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Workload (hours)


Master Laboratory 150 h (20 days*7.5 h)

90 h 240 h

Total: 150 h 90 h 240 h


Previous knowledge - Experimental skills as acquired e.g. in the Physics Laboratory B (B.Sc.) - Statistical methods of data analysis

Language English



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3.8. Research Traineeship (30 ECTS credit points)

Module 07LE33M-RTRAIN

Research Traineeship 30 ECTS

Responsibility / Supervision

Dean of Studies, Group leaders at the Institute of Physics and associated Institutes

Course details Type ECTS Assessment

Research (under supervision) 6 months 30 SL

Organisation Prior to their Master thesis students engage in a Research Traineeship which is accom-plished in a six-month period. The aim of this module is to acquire basic knowledge in a certain research topic and field in preparation for the subsequent Master Thesis. For the traineeship, students select a supervisor at the Institute of Physics or at one of the associated and participating research institutes. The research traineeship can be started any time and has a duration of exactly 6 months. The students have to register for the research traineeship at the examination office.

Grading ungraded


• Students have a specialized basic knowledge in a certain research topic. • Students know and are able to apply specific experimental and/or theoretical tools

and methods in a specialised field of research. • Students are prepared for performing a self-dependent research project (prepa-

ration for Master Thesis)

Course content • Students acquire basic knowledge in a certain field of research in preparation for their Master Thesis.

• Participants obtain training in applying experimental and/or theoretical tools in a specialized field of research.

• Students participate in a current research project under the supervision of lecturers and researchers (post-docs and doctoral researchers).

Workload (hours)

900 h distributed over a six-month period

Usability M.Sc. Physics, M.Sc Applied Physics

Precondition Admission to the Research Traineeship requires successful accomplishment of the module Master Laboratory and of three of the four marked courses (AR) of the modules Advanced Quantum Mechanics, Advanced Physics 1, Advanced Physics 2, and Term Paper.

Language English



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3.9. Master Thesis (30 ECTS credit points)

Module 07LE33M-MSC

Master Thesis 30 ECTS

Responsibility / Supervision

Group leaders at the Institute of Physics and associated Institutes

Module details Type ECTS Assessment

Master Thesis 6 months 28 PL: final thesis

Master Colloquium 45 min 2 SL: oral presentation

Total: 30

Organisation For their master thesis students select a supervisor at the Institute of Physics or at one of the associated and participating research institutes. Typically, the master thesis is pursued within the same work group as the traineeship. The Master Thesis starts at the latest 2 weeks after successful completion of the Research Traineeship. Registra-tion has to be arranged with the examination office.

Grading The final thesis is graded by two examiners. One examiner is the supervisor of the thesis. Both grades contribute equally to the final grade (arithmetic mean).


• Students acquired specialized knowledge of a certain research topic and field. • Students have a strong expertise in applying specific experimental and/or theoret-

ical tools and methods in their field of research. • Students are able to perform independent research and can critically evaluate and

assess their scientific results. • Students can search and read scientific literature and apply and relate reported

results to their research.

Module content • Acquiring in-depth knowledge in the field of the master thesis work. • Working on a particular problem in a specialized field of research. • Development of the required experimental and/or theoretical tools and methods. • Preparation of a written report on the performed research work. • Preparation and performance of an oral presentation in the form of a public collo-

quium, discussing the topic of the master thesis, its physical context, and the un-derlying physical concepts.

Workload (hours)

900 h distributed over a six-month period. This workload includes research, preparation of the written thesis and preparation of the final presentation.

Usability M.Sc. Physics, M.Sc Applied Physics

Precondition Admission to the Master Thesis requires successful accomplishment of the module Research Traineeship.

Language English or German



21

4. Advanced Physics Lectures

4.1. Advanced Atomic and Molecular Physics

Lecture 07LE33M-ADV_EXP_AMO

Advanced Atomic and Molecular Physics Adv. Experiment

Lecturer/s Lecturers from Experimental Atomic, Molecular and Optical Physics

Course details Type Credit hrs ECTS Assessment

Lecture and exercises (L+E) 4+2 9 SL or PL

Term In general the course will be offered each WiSe.


Students have a deeper understanding of both, the properties of matter based on the nature and interactions of atoms and molecules, and of current and future technolo-gies based on controlled quantum processes, such as employed in atomic clocks, atom interferometers, quantum optics and quantum computing, nanoscale engineer-ing, photochemistry and energy conversion.

Course content • Light-matter interaction: scattering, absorption and emission of light, dressed states, coherence, strong fields

• Scattering of atomic and molecular systems • Properties of diatomic molecules: vibrations and rotations • Properties of polyatomic molecules: electronic states, molecular symmetries,

chemical bonds • Modern AMO applications in science and technology

Previous knowledge Experimental Physics I-IV (B.Sc. Physik)

Workload (hours)


Lecture and exercises (L+E) 90 h 180 h 270 h

Usability M.Sc. Physics modules: “Advanced Physics 1+2” (PL), “Advanced Physics 3” (SL) or “Elective Subjects” (SL), M.Sc. Applied Physics modules: “Advanced Experimental Physics” (PL), “Applied Physics” (PL or SL) or “Elective Subjects” (SL)

Language English



22

4.2. Advanced Optics and Lasers

Lecture 07LE33M-ADV_EXP_OL

Advanced Optics and Lasers Adv. Experiment

Lecturer/s Lecturers from Experimental Atomic, Molecular and Optical Physics





• Students are familiar with the physical concepts of lasers and know the fundamen-tals of the interaction between laser light and matter.

• Students are able to describe in detail the inherent behaviour and functionality of the many different types of modern lasers.

• Students have a deep understanding of the properties of coherent laser light and are able to understand and analyse nonlinear optical effects, as e.g. induced by lasers in transparent materials.

Course content • Light-matter interaction: Absorption/emission, line broadening • Coherence and interference: temporal, spatial coherence, interferometers • The laser principle: 2, 3, 4-level lasers, rate equation models, output power of a

laser; • Optical resonators: transmission spectra, stability • Laser modes: Paraxial approximation, Gaussian beams, longitudinal and trans-

verse modes, mode selection • Short laser pulses: Dynamic solutions of rate equation, Q-switching, mode locking,

intense short pulses, generation of ultra-short laser pulses • Nonlinear optics: Second, third order polarizability, frequency conversion, optical

parametric amplification, high-harmonics generation


Workload (hours)




Language English



23

4.3. Condensed Matter I: Solid State Physics

Lecture 07LE33M-ADV_EXP_CM1

Condensed Matter I: Solid State Physics Adv. Experiment

Lecturer/s Lecturers from Experimental Condensed Matter and Applied Physics

Course details Form Credit hrs ECTS Assessment




• Students know the reciprocal space description of crystals and related quasiparti-cles like phonons

• Students know the quantum mechanical description of electrons in periodic poten-tials (Bloch- and Wannier-functions)

• Students have a good overview of experimental state of the art techniques for the study of the properties of solid state materials

• Students know how to obtain and are able to interprete experimental data like measurements of electronic band structures or phonon dispersion curves

• Students know about newer developments in the experimental characterization of many-body quantum effects like magnetism or superconductivity

Course content • Atomic structure of matter • lattice dynamics, phonons • electronic structure of materials • optical properties • magnetism/superconductivity


Workload (hours)




Language English



24

4.4. Condensed Matter II: Interfaces and Nanostructures

Lecture 07LE33M-ADV_EXP_CM2

Condensed Matter II: Adv. Experiment Interfaces and Nanostructures

Lecturer/s Lecturers from Experimental Condensed Matter and Applied Physics

Course details Form Credit hrs ECTS Assessment


Term In general the course will be offered each SoSe.


• Students are able to describe interaction forces at interfaces in terms of their range and their consequences on thermodynamic and kinetic properties.

• Students understand processes at surfaces like adsorption/desorption, surface re-construction, surface transport, or wettability.

• Students are able to describe processes as well as structural transitions at liquid, solid-liquid, and solid interfaces with respect to their hydrodynamic and electronic properties.

• Students know processes for preparing well defined and patterned surfaces. • Students identify the relevant processes for the formation of nanostructures and

structuring of surfaces at the nm-scale.

Course content • Surfaces and interface • structure formation on surfaces • self-assembly, morphology and transitions • optical and electronic properties


Workload (hours)




Language English



25

4.5. Advanced Particle Physics

Lecture 07LE33M-ADV_EXP_PP

Advanced Particle Physics Adv. Experiment

Lecturer/s Lecturers from Experimental Particle Physics





• Students know the guiding principle of internal symmetries and how discrete and local gauge theories are constructed. They are able to analyse the symmetries of a Lagrangian and understand the implications for the phenomenology.

• Students learn to discriminate different particles/processes via the characteristic signature in different detector components.

• Students know the interplay of model building and experimental findings. They are able to critically compare theoretical predictions with experimental findings.

• Students can perform simple cross section evaluations using Feynman calculus. • Students know the structure and phenomenology of the Standard Model of Particle

Physics and its limitations.

Course content • Quantum Electrodynamics as prototype of a local gauge theory: Feynman rules, calculation of matrix elements, higher order corrections, principle of renormalisa-tion, running coupling strength, basic experimental tests at low (g-2, Lamb shift) and high energies (PETRA, LEP colliders)

• Quantum Chromodynamics: phenomenological differences between abelian and non-abelian gauge theories, confinement, asymptotic freedom, stability of had-rons, jets, and basic experimental tests at PETRA, LEP, Tevatron and LHC.

• Parton density functions of the proton and its determination in deep inelastic scat-tering, Bjorken scaling and its violation.

• Electroweak theory and formulation of the Standard Model of particle physics: charged and neutral weak currents, from Fermi theory to the Glashow-Salam-Weinberg theory, massive weak gauge bosons, parity violation, CP violation, basic experimental tests at various colliders.

• Observation and phenomenology of neutrinos oscillations. • Electroweak symmetry breaking: Higgs mechanism, Higgs boson physics (exper-

imental aspects) • Limitations of the Standard Model (neutrinos masses, dark matter,…) and possi-

ble extensions (SUSY, extra dimensions,…)

Previous knowledge Experimental Physics V and Theoretical Physics IV (B.Sc. Physik)

Workload (hours)



Usability M.Sc. Physics modules: “Advanced Physics 1+2” (PL), “Advanced Physics 3” (SL) or “Elective Subjects” (SL),



26

M.Sc. Applied Physics modules: “Advanced Experimental Physics” (PL), “Applied Physics” (PL or SL) or “Elective Subjects” (SL)

Language English



27

4.6. Particle Detectors

Lecture 07LE33M-ADV_EXP_PDET

Particle Detectors Adv. Experiment




Term In general the course will be offered each WiSe


• Students are able to understand the physics of particle detection • Students are able to understand the different types of particle detectors • Students are able to design a particle detector for specific experiments

Course content • Interaction of particles with matter • General properties of particle detectors • Tracking detectors • Time measurement • Energy measurement • Particle identification • Electronics, trigger and data acquisition • Detector systems in Particle and Astroparticle Physics • Applications of particle detectors in medicine

Previous knowledge Experimental Physics V (B.Sc. Physik)

Workload (hours)




Language English



28

4.7. Hadron Collider Physics

Lecture 07LE33M-ADV_EXP_HCP

Hadron Collider Physics Adv. Experiment




Term In general the course will be offered each SoSe


• Students acquire the basic experimental concepts of experiments at hadron collid-ers (detector and trigger concept, soft and hard collisions, underlying event, pile-up)

• Students know the concept of cross section calculations at hadron colliders from first principles (Feynman diagrams) and from numerical calculations using Monte Carlo generators

• Students know the concepts of tests of the Standard Model at hadron colliders, including precision measurements in some areas

• Students acquire deeper insight and familiarize with modern multivariate tech-niques for the separation of signal and background processes in the search for new physics / deviations from the Standard Model

• Students know the up-to-date status on experimental tests of the • Standard Model and on Searches for New Physics

Course content • Introduction to accelerators, with focus on the Large Hadron Collider • Detector and trigger concepts of hadron collider experiments • Phenomenology of pp collisions • Structure functions, calculation of cross sections, Monte Carlo generators for pp

collisions • Particle signatures in LHC experiments • pp collisions with low transverse momentum (underlying event, minimum bias) • Test of QCD at hadron colliders (jet production, top quark production, W/Z + jet

production) • Measurements of important parameters of the Standard Model (m_t, m_W, gauge

couplings, ..) • Physics of heavy quarks (b-physics, the top quark and its properties) • Higgs boson physics (experimental detection, measurements of Higgs boson prop-

erties, additional Higgs bosons,..) • Search for supersymmetric particles • Search for other extensions of the Standard Model

Previous knowledge Experimental Physics V (Nuclear and Particle Physics, B.Sc. Physik) Advanced Particle Physics (desirable, MSc Physics)

Workload (hours)





29

Usability M.Sc. Physics modules: “Advanced Physics 1+2” (PL), “Advanced Physics 3” (SL) or “Elective Subjects” (SL)

Language English



30

4.8. Astroparticle Physics

Lecture 07LE33M-ADV_EXP_APART

Astroparticle Physics Adv. Experiment


Course details Type Credit hrs E CTS Assessment


Term The lecture is offered on an irregular basis.


• Students are familiar with the standard models of particle physics and cosmology • Students acquire an understanding of the physics of the early universe • Students know the characteristics of the energy density in the universe • Students are familiar with up-to-date research on dark matter and dark energy • Students acquire insight on nuclear fusion and the evolution of stars • Students have knowledge of the nature of cosmic rays

Course content • The standard model of particle physics • Conservation Rules and symmetries • The expanding universe • Matter, Radiation • Dark matter • Dark energy • Development of structure in the early universe • Particle physics in the stars • Nature and sources of high energy cosmic particles • Gamma ray and neutrino astronomy

Previous knowledge Experimental Physics V (B.Sc. Physik)

Workload (hours)




Language English



31

4.9. Theoretical Condensed Matter Physics

Lecture 07LE33M-ADV_THEO_CONDMAT

Theoretical Condensed Matter Physics Adv. Theory

Lecturer/s Lecturers from Theoretical Condensed Matter and Applied Physics





• Students are familiar with the relevant theoretical concepts in Condensed Matter Physics.

• Students are able to calculate physical properties of various condensed matter systems based on quantum mechanics, and appreciate the physical ideas behind these approximation schemes, as well as their limitations.

Course content • Crystal structures, crystal vibrations, quantization of harmonically coupled lattices, phonons.

• Electrons in periodic potentials, Bloch waves, band structure. Application to con-ductors, insulators and semi-conductors.

• Electron phonon coupling. BCS theory of superconductivity. • Spin degrees of freedom. Classical and quantum spin chains.

Previous knowledge Theoretical Physics I-V (B.Sc. Physik)

Workload (hours)



Usability M.Sc. Physics modules: “Advanced Physics 1+2” (PL), “Advanced Physics 3” (SL) or “Elective Subjects” (SL), M.Sc. Applied Physics modules: “Advanced Experimental Physics” (PL) or “Elective Subjects” (SL)

Language English



32

4.10. Classical Complex Systems

Lecture 07LE33M-ADV_THEO_CS

Classical Complex Systems Adv. Theory

Lecturer/s Lecturers from Theoretical Atomic, Molecular and Optical Sciences or from Theoretical Condensed Matter and Applied Physics





• Students are familiar with stochastic and deterministic concepts to model complex systems.

• Students are capable of recognizing and rigorously describing phenomena com-monly encountered in complex systems.

• Students are able to use probabilistic notions to model systems subject to uncer-tainty about their microscopic states and laws.

• Students are able to run and interpret Monte Carlo computer simulations as well as to quantify the confidence in results produced by randomized algorithms.

• Students are able to use basic statistical tools to infer probabilistic statements from empirical observations.

Course content The first two thirds of the lecture cover basic theory, while the final third is concerned with concrete applications. Topics treated in the latter part depend more strongly on the lecturer. Stochastic Processes:

• Random walks, Markov model • Stochastic differential equations and master equations

(Langevin- and Fokker-Planck Equation) • Numerical treatment and Monte Carlo techniques

Non-Linear Dynamics / Chaos Theory:

• Dynamical systems (discrete, differential equations, Hamiltonian) • Lyapunov exponents • Attractors and bifurcations

Applications:

Molecular dynamics simulations • Molecular driving forces and force field models • Simulation techniques and sampling • Energy landscapes and analysis of dynamics

Time series analysis and inverse problems • Estimation and test theory • Spectral analysis • State space model



33

Previous knowledge Theoretical Physics I-V (B.Sc. Physik)

Workload (hours)




Language English



34

4.11. Complex Quantum Systems

Lecture 07LE33M-ADV_THEO_OS

Complex Quantum Systems Adv. Theory

Lecturer/s Lecturers from Theoretical Atomic, Molecular and Optical Sciences or from Theoretical Condensed Matter and Applied Physics



Term Lecture is offered on an irregular basis.


• The students know the advanced physical concepts and mathematical techniques in the field of complex and open quantum systems;

• They have the ability to apply these concepts and techniques to the theoretical modelling and analysis of specific complex systems and to derive emergent phe-nomena in open systems (e.g. macroscopic classicality) from microscopic laws of quantum mechanics (e.g. decoherence).

• For structural track: The students know how to reason about counter-intuitive as-pects of quantum theory using mathematically rigorous notions.

Course content • Quantum states: Pure and mixed states, density matrices, quantum state space • Composite quantum systems: Tensor product, entangled states, partial trace and

reduced density matrix, quantum entropy • Open quantum systems: Closed and open systems, dynamical maps, quantum

operations, complete positivity and Kraus representation • Dynamical semigroups and quantum master equations: Semigroups and genera-

tors, quantum Markovian master equations, Lindblad theorem • General properties of the master equation: Dynamics of populations and coher-

ences, Pauli master equation, relaxation to equilibrium • Decoherence: Destruction of quantum coherence through interaction with an en-

vironment, decoherence versus relaxation Applied Track: • Microscopic theory: System-reservoir models, Born-Markov approximation, micro-

scopic derivation of the master equation. • Applications: Quantum theory of the laser, superradiance, quantum transport,

quantum Boltzmann equation Structural Track: • Uncertainty relations: Joint measurability, uncertainty relations for continuous and

discrete observables, information-disturbance tradeoff • Contextuality: Non-Locality, Bell's Theorem, Marginals

Previous knowledge Theoretical Physics IV (Quantum Mechanics, B.Sc. Physik) and Advanced Quantum Mechanics (M.Sc. Physics)



35

Workload (hours)




Language English



36

4.12. Quantum Field Theory

Lecture 07LE33M-ADV_THEO_QFT

Quantum Field Theory Adv. Theory

Lecturer/s Lecturers from Theoretical Particle Physics





• Students are able to write down the Lagrange function for the standard field theories (scalar, Dirac and gauge theories).

• They are familiar with concepts of canonical relativistic field quantization. • They can derive the Feynman rules for perturbative expansions from a given Lagran-

gian and are able to construct Feynman diagrams. • They can apply the standard methods for evaluating Feynman diagrams in Born ap-

proximation. • They are familiar with quantum electrodynamics and its phenomenology.

Course content • Classical field theory, Lagrange formalism • Relativistic wave equations: Klein-Gordon, Dirac, Maxwell, Proca equations • Basics of Lie Groups, Lorentz group and its representations, Poincare group and its

representations • Canonical quantisation of free fields (scalar, Dirac, vector fields), causal propagator • Interacting fields, gauge theories • Scattering theory, S-matrix • Perturbation theory, Wick’s theorem, and Feynman diagrams • Quantum electrodynamics and phenomenological applications (Compton scattering,

pair creation and annihilation, Bhabha scattering in Born approximation) • Optional: Functional Integrals, generating functionals, Grassman variables for fermi-

onic fields • Optional: Introduction to higher perturbative orders

Previous knowledge Electrodynamics, quantum mechanics, special relativity

Workload (hours)




Language English



37

4.13. General Relativity

Lecture 07LE33M-ADV_THEO_GR

General Relativity Adv. Theory






• Students know the fundamentals of special and general relativity, Lorentz trans-formations, Poincare-group. They can explain the fundamental phenomena re-lated to relativity (perihel rotation of Mercury, relativistic Doppler effects, influence of gravity on clocks, accelerated systems).

• They know the mathematical foundations of Riemannian geometry and know to interpret and obtain the metric, Christoffel symbols and Riemannian curvature components for simple geometric structures.

• They can derive the geodesic equation from the action principle and know its rela-tion to parallel transport. They can find geodesics in simple geometries.

• They know how to calculate the energy-momentum tensor from a given field the-ory, for free particles and for collective systems (radiation dominated or matter dominated homogeneous universes).

• They know how to read and construct space-time diagrams (Finkelstein, Kruskal, Carter-Penrose) for classical geometries (Minkowski space, Rindler space, Schwarzschild and Kerr geometries).

Course content • Equivalence principles: Minkowski space, Poincare group, space-time diagrams, world lines, proper time and distance, application to simple phenomena (elevator thought experiments, twin paradox, relativistic Doppler effect, accelerated sys-tems), Lorentz transformations and general coordinate transformations.

• Differential geometry: manifolds and tangent spaces, forms, metric tensor, integra-tion, Stoke’s theorem, outer derivative, Lie derivative, covariant derivative and Christoffel symbols, parallel transport, geodesics, curvature (Riemann tensor, Weyl tensor, Ricci tensor and scalar), torsion, Killing vectors, Riemann coordi-nates.

• Dynamics of the gravitational field: Einstein equations, cosmological constant, en-ergy-momentum tensor of matter systems (perfect fluids, point particles, Klein-Gordon and Maxwell theory).

• Effects based on post-Newtonian approximations: red/blue shift effects, rotation of the perihel, effect of gravitation on clocks, deflection of light.

• Gravitational waves: perturbative expansion of field equations, gauge invariance, origin and detection of gravitational waves.

• Classical space times: Minkowski, Rindler, Schwarzschild, Kerr, Reissner-Nordstrøm, Kerr-Newman geometries; Robertson-Walker metrics, Friedmann uni-verses and deSitter space. Discussion of causal structure, geodesic complete-ness, key coordinate systems and Carter-Penrose diagrams.

• Optional: Einstein-Hilbert action and variational principle. • Optional: Modern topics in cosmology: CMB, the Inflation Model.



38

Previous knowledge Electrodynamics, special relativity, Lagrangian mechanics

Workload (hours)




Language English



39

4.14. Quantum Optics

Lecture 07LE33M-ADV_THEO_QO

Theoretical Quantum Optics Adv. Theory

Lecturer/s Lecturers from Theoretical Atomic, Molecular and Optical Physics



Term Lecture is offered on an irregular basis.


• Students are able to characterize the quantum state of the electromagnetic field • Students are able to interpret the dynamics of the quantized field in terms of canoni-

cally conjugate variables • Students are able to distinguish classical from quantum features of the quantized

field, and to perform the classical limit • Students are able to infer the quantum state of the light field from multi-point corre-

lation functions • Students are able to describe the quantum state of strongly coupled light-matter sys-

tems • Students are able to give a semiclassical description of light-matter systems • Students are familiar with a selection of paradigmatic experimental settings to probe

generic quantum properties of the light field

Course content • Quantization of the radiation field • Coherent states • Phase space representation of quantum states • Counting statistics • Dressed states • Floquet theory • Special topics, e.g. micromaser theory, elements of entanglement theory, laser the-

ory, master equations, coherent control • Light-matter interaction

Previous knowledge Introductory courses of experimental and theoretical physics (mechanics, electrody-namics, quantum mechanics)

Workload (hours)




Language English



40

4.15. Quantum Chromodynamics

Lecture 07LE33M-ADV_THEO_QCDCOLL

Quantum Chromodynamics Adv. Theory and Collider Physics






• Students are able to construct Lagrangians for (abelian and non-abelian gauge theories).

• They are familiar with the concepts of field quantization via functional integrals, the concept of Green functions and of their gauge symmetries.

• They can evaluate gauge theories perturbatively at the one-loop level, including renormalization.

• They know quantum chromodynamics and its basic phenomenology. • They are prepared to work on experimental or theoretical research at particle col-

liders such as the CERN Large Hadron Collider (LHC).

Course content • Quantization of field theories via functional integrals • Perturbation theory and Feynman diagrams • Gauge theories and their quantization • BRS symmetry and Slavnov-Taylor identities • Gauge theory of strong interaction (quantum chromodynamics) • Quantum corrections, regularization, and renormalization • Renormalization group equations • Jet produktion in e+e- annihilation • Parton model for hadronic particle reactions • Parton distribution function and DGLAP evolution • Deep inelastic electron-nucleon scattering • Quantum corrections to the Drell-Yan process

Previous knowledge Electrodynamics, quantum mechanics, relativistic quantum field theory

Workload (hours)




Language English



41

4.16. Computational Physics: Materials Science

Lecture 07LE33V-ADV_THEO_COMPPHYS

Computational Physics: Materials Science Adv. Theory

Lecturer/s Lecturers from Computational Physics





• Students have understood the basic Hamiltonian of CMS • Students are familiar with the various approximations that lead to different methods

in CMS: Born-Oppenheimer approximation, classical approximation for the nuclei, local density approximation, tight-binding, semi-empirical interatomic potentials, coarse grained models, hydrodynamic limit

• Students have a basic knowledge of density functional theory. • Students can set up simple molecular dynamics calculations. • Students are familiar with the different types of Born-Oppenheimer surfaces for the

different types of interatomic binding. • Students are familiar with extended molecular dynamics methods.

Course content This lecture provides an introduction into basic concepts of atomistic computational materials science. The computational tools for different time and length scales will be introduced and it will be discussed how these tools can be combined in order to solve physical problems extending over too many scales for one single method alone. We will start with a brief introduction to density functional theory and more approximate methods such as tight binding. Quantum derived forces can be extracted from these methods and the short term dynamics of small nanosystems can be studied. For the simulation of larger systems and longer time scales, classical interatomic potentials are required. The students will become familiar with some examples for the different types of interatomic potentials: e.g. Lennard-Jones, Born-Mayer, Embedded-Atom, Bond-Order-potentials as well as bead-spring potentials for polymers. A brief intro-duction into the basic methodology of micro-canonical and thermostated molecular dynamics simulations will be given. The lecture is accompanied by a hands-on programming course. Classical molecular dynamics simulations will be used to study metallic and covalently bonded materials.

Previous knowledge Basic knowledge in classical and quantum mechanics

Workload (hours)



Usability M.Sc. Physics modules: “Advanced Physics 1+2” (PL), “Advanced Physics 3” (SL) or “Elective Subjects” (SL),



42

M.Sc. Applied Physics modules: “Advanced Theoretical Physics” (PL), “Applied Phys-ics” (PL or SL), “Elective Subjects” (SL)

Language English



43

5. Elective Subjects

5.1. Microscopy and Optical Image Formation (7 ECTS)

Module no. 07LE33M-MOIF

Microscopy and Optical Image Formation 7 ECTS

Lecturer/s Prof. Dr. Alexander Rohrbach



Term The lecture is offered in the winter semester


The student should learn how to guide light through optical systems, how optical infor-mation can be described very advantageously by three-dimensional transfer functions in Fourier space, how phase information can be transformed to amplitude information to generate image contrast. Furthermore one should experience that wave diffraction is not reducing the information and how to circumvent the optical resolution limit. The student should learn to distinguish between coherent and incoherent imaging, learn about modern techniques using self-reconstructing laser beams, two photon excitation, fluorophores depletion through stimulated emission (STED) or multi-wave mixing by coherent anti-Stokes Raman scattering (CPLS). The tutorials help the student to get a more in depth and thorough under-standing of the lecture. Here, a special focus is put on the transfer of knowledge obtained in the lecture. To achieve this, the students should pre-pare weekly exercise and present them during the tutorial. Difficult exercises are presented by the tutors.

Course content The scientific breakthroughs and technological developments in optical microscopy and imaging have experienced a real revolution over the last 10-15 years. Hence, the 2014 Nobel-Prize for super-resolution microscopy could be seen as a logical consequence. This lecture gives an overview about physical principles and techniques used in modern photonic imaging. Topics: 1. Microscopy: History, Presence and Future 2. Wave- and Fourier-Optics 3. Three-dimensional optical imaging and information transfer 4. Contrast enhancement by Fourier-filtering 5. Fluorescence – Basics and techniques 6. Point scanning and confocal microscopy 7. Microscopy with self-reconstructing beams 8. Optical tomography 9. Nearfield and Evanescent Field Microscopy 10. Super-resolution using structured illumination 11. Multi-Photon-Microscopy 12. Super resolution imaging by switching single molecules The lecture has an ongoing emphasis on applications, but nevertheless presents a mixture of fundamental physics, compact mathematical descriptions and many exam-ples and illustrations. The lecture aims to encompass the current state of a scientific



44

field, which will influence the fields of nanotechnology and biology/medicine quite sig-nificantly.

Literature Accompanying to the lecture printed lecture notes with defined gaps (white boxes) are distributed. Optical Microscopy: • Jerome Mertz: Introduction to Optical Microscopy, Roberts & Co Publ. 2009 • U. Kubitschek, Fluorescence Microscopy, Wiley-Blackwell 2013 • Min Gu, Advanced optical imaging theory, Springer - Berlin, 1999 • James B. Pawley: Handbook of Biological Confocal Microscopy , Springer - Berlin,

2006 • Herbert Gross: Handbook of optical systems, Vol 2: Physical image formation,

Wiley VCH 2005 General Optics: • Hecht, E. (2002). Optics, Addison Wesley. • Saleh, B. E. A. and M. C. Teich (1991). Fundamentals of Photonics, Wiley &

Sons,Inc. • Herbert Gross: Handbook of optical systems, Vol 1-5

Preliminaries / Previous knowledge

Final Exam Written or oral exam (120 min)

Workload (hours)



Usability M.Sc. Physics: “Elective Subjects” (SL), M.Sc. Applied Physics: “Applied Physics” (PL or SL) or “Elective Subjects” (SL)

Language English



45

5.2. Biophysik - Grundlagen und Konzepte / Biophysics - Basics and concepts (7 ECTS)

Module no. 07LE33M-BIOPHYS

Biophysik - Grundlagen und Konzepte / Biophysics - Basics and concepts 7 ECTS






This lecture gives a survey through modern cell biophysics, addresses state of the art scientific questions and presents modern investigation methods. This comprises clas-sical but also novel physical methods and theories, which pushed the field of biophysics together with newest measurement technology. The applied physical methods do not only inspire biology and medicine, but also the physics of complex systems, which achieves an unequaled level of self-organisation and complexity inside living cells. This lecture is designed for physicists and engineers and provides a colourful mixture of physics, biology, chemistry, mathematics, and engineering that is illustrated with nu-merous pictures and animations. The tutorials help the students to get a more in depth and thorough under-standing of the lecture. Here, a special focus is put on the transfer of knowledge obtained in the lecture. To achieve this the students should pre-pare weekly exercise and present them during the tutorial. Only difficult exercises are presented by the tutors.

Course content Topics: 1. Structure of the cell or the recipe for cell-biophysical science 2. Diffusion and Fluctuation 3. Sensing and Acting measurement principles 4. Biologically relevant forces 5. Biophysics of proteins 6. Polymer physics 7. Visco-elasticity and micro-rheology 8. Dynamics of the cytoskeleton 9. Molecular motors 10. Membrane biophysics

Literature • Accompanying to the lecture printed lecture notes with defined gaps (white boxes) are distributed.

• Rob Phillips: Physical Biology of the Cell • Joe Howard: Mechanics of Motor Proteins and the Cytoskeleton • Gary Boal: Mechanics of the Cell

Erich Sackmann & Rudolf Merkel: Lehrbuch der Biophysik




46

Workload (hours)




Language German



47

5.3. Nano-Photonics - Optical manipulation and particle dynamics (7 ECTS)

Module no. 07LE33M-NANOOPT

Nano-Photonics - Optical manipulation and particle dynamics 7 ECTS




Term The lecture is offered in the summer semester


Optical traps and optical micro-manipulation techniques do have the potential to play a key role in future micro- and nano-systems in conjunction with the life sciences. In this lecture the students should learn what is doable with optical forces, where physical limits are and what is limited by nowadays technology. Besides fascinating fundamental research various applications related to biology or fluctuation based systems are pre-sented. The lecture is manifold and teaches basics in optics, statistical physics and biology/biophysics. The tutorials help the students to get a more in depth and thorough under-standing of the lecture. Here, a special focus is put on the transfer of knowledge obtained in the lecture. To achieve this the students should pre-pare weekly exercise and present them during the tutorial. Only difficult exercises are presented by the tutors.

Course content 1. Introduction 2. Light - Information carrier and actor 3. About microscopy 4. Light scattering 5. Optical forces 6. Tracking beyond the uncertainty 7. Brownian motion and calibration techniques 8. Photonic force microscopy 9. Applications in cell biophysics 10. Time-multiplexing and holographics optical traps 11. Applications in microsystems technology 12. Applications in nanotechnology

Literature Accompanying to the lecture printed lecture notes with defined gaps (white boxes) are distributed. General optics: • Hecht, E. (2002). Optics, Addison Wesley. • Saleh, B. E. A. and M. C. Teich (1991). Fundamentals of Photonics, Wiley & Sons,

Inc. Nano optics • L. Novotny & B. Hecht, E. (2002). Principles of Optics, Cambridge.

Statistical physics and thermodynamics • Standard text books



48

Chemical and biological forces and interactions Leckband, D. & J. Israelachvili (2001). "Intermolecular forces in biology." Quart. Rev. Biophys 34: 105–267


Workload (hours)




Language English



49

5.4. Wave Optics (7 ECTS)

Module no. 11LE50MO-5221S

Wave Optics 7 ECTS






The goal of this lecture is to teach the students how light interacts with small structures and how optical systems guide light. The students will start at Maxwell's equations and move on to the description of light as photon or wave, depending on the given problem. Furthermore, the close connection between spatial and temporal coherence, interfer-ence and holography is demonstrated. The last chapter teaches concepts of linear and non-linear light scattering, as well as the most important plasmonic effects. In total, the students learn how to shape light in three dimensions and how optical problems that arise in research and development are solved.

Course content 1. Introduction Some motivation, literature and a bit of history 2. From Electromagnetic Theory to Optics What is light? Which illustrative pictures do the Maxwell equations provide? If matter, dielectric and metallic, consists of coupled, damped springs (harmonic oscillators), how does matter depend on the frequency of light? What do the wave equation and the Helmholtz equation express and how can one handle waves in position space and fre-quency space. 3. Fourier-Optics How does a wave transform position information into directional information? Why can this be well described by Fourier transformations in 1D, 2D and 3D? What has this to do with linear optical system theory including spatial frequency filters and the sampling theorem? 4. Wave-optical Light Propagation and Diffraction Different methods are introduced of how to describe the propagation of ways in position space and frequency space. We do the direct transfer from propagation to diffraction of light and momentum space. We treat evanescent waves, thin diffracted objects, the propagation of light in inhomogeneous media and the diffraction at gratings. This allows to discuss important active elements such as acousto-optic and spatial light modulators. We end with adaptive optics and phase conjugation. 5. Interference, Coherence and Holography We learn how a composition of k-vectors defines the phases of interfering waves and the resulting stripe patterns. The relative phases of each partial wave in space and time change the interference significantly and define the coherence of light - these concepts will be discussed in detail. We learn how to write and read phase information in holog-raphy.



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6. Light Scattering and Plasmonics The interaction of light with matter is based on particle scattering: we discuss the theo-retical concepts of light scattering on the background of Fourier theory. We expend these approaches to photon diffusion, nonlinear optics, fluorescence and Raman scat-tering or scattering at semiconductor quantum dots - which are all hot topics in modern Photonics. A big emphasis is put on the description of surface plasmons and particle plasmons, where light can be extremely confined. 1. Introduction

1.1. Motivation 1.2. Literature 1.3. A bit of history

2. From Electromagnetic Theory to Optics 2.1. What is Light? 2.2. The Maxwell-equations 2.3. The change of Light in Matter 2.4. Wave equation and Helmholtz equation 2.5. Waves in position space and frequency space

3. Fourier-Optics 3.1. Introduction 3.2. The Fourier-Transformation 3.3. Linear Optical Systems 3.4. Spatial frequency filters 3.5. The Sampling Theorem

4. Wave-optical Light Propagation and Diffraction 4.1. Paraxial light propagation by Gaussian beams 4.2. Wave Propagation and Diffraction 4.3. Evanescent waves 4.4. Diffraction at thin Phase and Amplitude Objects 4.5. Light Propagation in inhomogeneous Media 4.6. Diffraction at gratings 4.7. Acousto-Optics 4.8. Spatial Light Modulators 4.9. Adaptive Optics and Phase Conjugation

5. Interference, coherence and holography 5.1. Some Basics 5.2. Interferometry 5.3. Foundations of Coherence Theory 5.4. Principles of Holography

6. Light Scattering and Plasmonics 6.1. Scattering of light at particles 6.2. Photon Diffusion 6.3. Basics of Nonlinear Optics 6.4. Fluorescence und Raman-scattering 6.5. Fluorescing quantum dots

6.6. Surface Plasmons and Particle Plasmons

Literature Accompanying to the lecture printed lecture notes with defined gaps (white boxes) are distributed.


Workload (hours)





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Language English



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5.5. Laser-based Spectroscopy and Analytical Methods (5 ECTS)

Module no. 07LE33M-LSPEC

Laser-based Spectroscopy and Analytical Methods 5 ECTS

Lecturer/s PD Dr. Frank Kühnemann (Fraunhofer IPM)





At the end of the course, the students • Will have knowledge about laser-based spectroscopic methods, particularly with

respect to analytical applications. • Will understand the physical principles of tuneable laser operation. • Will be enabled to evaluate the fundamental and practical limitations of detection

techniques. • Will have insight into development processes necessary to transfer a scientific

method into a practical tool for industrial environments. • Will be trained in the preparation and presentation of scientific talks.

Course content Lasers did become a powerful tool for measurement applications in areas like industry, medicine, or environment. The current course focuses on the use of tuneable lasers to interrogate the spectral “fingerprints” of gases, liquids and solids for analytical pur-poses. Typical examples are air quality monitoring or process control in industry. The lecture block in the first half of the course will give a comprehensive introduction into the following topics • Infrared molecular spectra • Tuneable lasers • Spectroscopic techniques (absorption, photoacoustic spectroscopy, cavity-based

methods) • Background signals, noise and detection limits

The seminar talks in the second block will focus on the application of different spectro-scopic methods for analytical tasks. At the start of the course, students will choose from a list of provided topics to prepare a talk and a short written summary. The preparation will be supported by topical literature and discussion sessions with the course staff. Duration of the talks will be approximately 30 minutes, followed by a discussion of content and presentation style.

Literature • lecture script • recommended literature will be announced in the lecture


Advanced Optics and Lasers

Final Exam Oral (graded seminar talk) and written (talk summary)



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Workload (hours)




Language English



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5.6. Photovoltaic Energy Conversion (5 ECTS)

Module no. 07LE33M- PHOTOVOLT

Photovoltaic Energy Conversion 5 ECTS

Lecturer/s Dr. Uli Würfel (Fraunhofer ISE)





• Students have a profound understanding of the working principles of solar cells and are thus able to apply these principles to different kinds of solar cell configurations

• Students are familiar with state of the art solar cells, the processes limiting their conversion efficiency, how these factors can be identified and if they could (in prin-ciple) be overcome

Course content • Fundamentals of semiconductors, intrinsic and extrinsic, Fermi-Dirac statistics, bands

• Generation, recombination and transport of charge carriers • Lifetime, diffusion length, pn-junction, ideal solar cell • Real solar cell structures, carrier selectivity & semi-permeable membranes • Characterisation methods

Overview about different PV technologies: Si-based, thin film, Organic, Perovskite, Concentrator-PV

Literature • lecture script • P. Würfel, Physics of Solar Cells, 2nd edition 2009, Wiley VCH


Basic knowledge of semiconductor physics is helpful but not mandatory

Final Exam Written exam (120 min) or oral exam (30 min)

Workload (hours)




Language English



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5.7. Multi-junction solar cell technology and concentrator photovoltaic (3 ECTS)

Module no. 11LE68MO-4103

Multi-junction solar cell technology and concentrator photovoltaic 3 ECTS

Lecturer/s Prof. Dr. Andreas Bett (Fraunhofer ISE)


Lecture and exercises (L) 2 3 SL



Course content • multi-junction solar cell approach to increase the sunlight conversion efficiency, different solar cell architectures

• introduction III-V materials, adjustment of band-gap, growth techniques • methods for characterisation of III-V materials and multi-junction solar cells • PV concentrator technology: low and high concentration • components of CPV systems: optics, cells, manufacturing • CPV system analysis including an economical evaluation

Literature • "Solar Cells and Their Applications", L. Fraas, L.Partain, Wiley, 2010; • "Advanced Concepts in Photovoltaics", AJ Nozik, G. Conibeer, MC Beard, Royal

Society of Chemistry, 2014; • "Next Generation Photovoltaics", AB Cristobal Lopez, A. Marti Vega, A. Luque

Lopez, Springer Series in Optical Sciences 165, 2012, • "Concentrator Phtovoltaics", A Luque, V. Andreev, Springer Verlag, Series in Op-

tical Sciences, 2011


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Final Exam -

Workload (hours)


Lecture and exercises (L) 30 h 60 h 90 h

Usability M.Sc. Physics: “Elective Subjects” (SL), M.Sc. Applied Physics: “Applied Physics” (SL) or “Elective Subjects” (SL)

Language English



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5.8. Solar Physics (5 ECTS)

Module no. 07LE33M-SOLPHYS

Solar Physics 5 ECTS

Lecturer/s Prof. Dr. Oskar von der Lühe (Kiepenheuer-Inst. for Solar Physics, KIS)

Course details Examination Credit hrs ECTS Assessment

Lecture and exercises (L) 2+1 5 SL or PL

Term The lecture is offered every second winter semester.


• Students obtain advanced knowledge about the Sun as a template star and as a complex physical system. Students also obtain knowledge about modern tools to research the Sun and their physical basis.

• Students understand the role of the Sun as the central component of the Solar system, its interaction with the heliosphere, and its impact on the near-Earth envi-ronment, the Earth’s climate and on modern civilization.

Course content • The Sun in the astrophysical context • Internal structure of the Sun • Solar rotation, convection and magnetism • The solar atmosphere • Chromosphere, corona and the solar wind • Sun – Earth interaction and space weather • The Why’s and How’s of solar observations

Literature • M. Stix, The Sun – An Introduction (2nd Ed.), Springer • P. Foukal, Solar Astrophysics (3rd Ed.), Wiley • Lecture Script (through ILIAS)


Experimental Physics I – IV. Completion of an introductory course on astrophysics (e.g. bachelor course) is highly recommended.

Final Exam Regular participation in exercises (SL) Written (120 min) or oral (30 min) exam (PL)

Workload (hours)




Language English



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5.9. Modern Astronomical Instrumentation (5 ECTS)

Module no. 07LE33M-ASTRINST

Modern Astronomical Instrumentation 5 ECTS

Lecturer/s Prof. Dr. Oskar von der Lühe (Kiepenheuer-Inst. for Solar Physics, KIS)



Term The lecture is offered every second winter semester.


• Students obtain an overview of observing facilities and instruments in which are used for astronomy to observe the e. m. spectrum, astroparticles and gravitational waves

• Students understand the design principles of optical instruments in general and obtain an introduction to modern lens design

Course content • Introduction to geometrical optics and aberration theory • Design and construction of astronomical telescopes for the whole spec-

trum of e. m. waves on the ground and in space • Post-focus instrumentation for astronomical telescopes • Spectroscopy and polarimetry • Detectors for astronomy • Radio telescopes • Detection of astroparticles and gravitational waves.

Literature • P. Léna, Observational Astrophysics, Springer • Landolt - Börnstein Group VI Vol. 4 Astronomy, Springer • Lecture Script (through ILIAS)


Experimental Physics I – IV. Completion of an introductory course on astrophysics (e.g. bachelor course) is highly recommended.

Final Exam Regular participation in exercises (SL) Written (120 min) or oral (30 min) exam (PL)

Workload (hours)




Language English



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5.10. Dynamic Systems in Biology (7 ECTS)

Module no. 07LE33M-DYNBIO

Dynamic Systems in Biology 7 ECTS

Lecturer/s Prof. Dr. Jens Timmer



Term The lecture is offered irregularly


• Students are familiar with classical and modern dynamic systems in biology.

• Students are able to mathematically formulate dynamic systems in biology as differential equations and implement these on the computer.

Course content • Numerical integration of differential equations • Mathematical biology • Population models • Hodgkin-Huxley model • Turing model • Enzyme kinetics • Systems biology • Metabolism • Signal transduction • Gene regulation

Literature • J.D. Murray. Mathematical Biology, Springer


Basics of Analysis and Linear Algebra

Final Exam Written (120 min) or oral (30 min) exam

Workload (hours)




Language English



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5.11. Molecular Dynamics & Spectroscopy (7 ECTS)

Module no. 07LE33M- MOLDYN

Molecular Dynamics & Spectroscopy 7 ECTS

Lecturer/s Prof. Dr. Gerhard Stock





Course content • Time-Dependent Quantum Dynamics • Density Matrix Theory • Quantum-Classical Formulation • Linear Spectroscopy • Nonlinear Techniques • Multidimensional Spectroscopy

Literature • P. Hamm, M. Zanni, Concepts and Methods of 2D Infrared Spectroscopy, Cam-bridge University Press, 2011

• V. May, O. Kühn, Charge and Energy Transfer Dynamics in Molecular Systems, Wiley-VCH, 2004

• S. Mukamel, Principles of Nonlinear Optical Spectroscopy, Oxford University Press, 1995



Workload (hours)




Language English



60

5.12. Physics of Nano-Biosystems (5 ECTS)

Module no. 07LE33M-NANOBIO

Physics of Nano-Biosystems 5 ECTS

Lecturer/s Prof. Dr. Thorsten Hugel (Faculty of Chemistry), Dr. Thomas Pfohl



Term The lecture is offered regularly in the summer semester.


• Students have a profound knowledge of the physical principles that govern biolog-ical systems in particular molecular machines.

• Students are familiar with the experimental methods to study biological systems in particular molecular machines.

• In the tutorials the students gain an in-depth understanding of of the lecture and discuss most recent literature.

Course content • Fundamental forces in Nano-Biosystems (elastic, viscous, thermal, chemical, en-tropic, polymerization)

• Concepts of equilibrium and non-equilibrium systems and measurements • Jarzynski equation • Linear and rotational molecular motors • Molecular details of muscle function • Optical and magnetic tweezers, AFM • Single molecule force spectroscopy • Single molecule fluorescence • Concepts of nanotribology and biolubrication

Literature • Jonathon Howard: “Mechanics of Motor Proteins and the Cytoskeleton“ (2005) • Phil Nelson: "Biological Physics: Energy, Information, Life" (2003) • Rob Philips, Jane Kondev, Julie Theriot, Hernan Garcia: "Physical Biology of the

Cell" (2012) • Recent journal publications

Previous knowledge Basic knowledge of statistics and optics is helpful but not mandatory.

Final Exam Written (120 min) or oral exam (30 min)

Workload (hours)




Language English



61

5.13. Physics of Medical Imaging Methods (5 ECTS)

Module no. 07LE33M-PHYSMED

Physics of Medical Imaging Methods 5 ECTS

Lecturer/s Prof. Dr. Michael Bock (Universitäts Klinikum)



Term The lecture is offered regularly in the winter semester.


• Students are able to distinguish and describe the physical basis of currently ap-plied medical imaging methods

• Students will become familiar with recent developments in medical imaging tech-nology and their clinical application

Course content Medical imaging is becoming increasingly important in the detection of disease, in the management of the patients, and in the monitoring of a therapy. In this lecture the physical basics of different medical imaging technologies will be presented, and different clinical application scenarios will be discussed. The following topics will be addressed: • overview over the physics of medical imaging • Magnetic Resonance Imaging (MRI)

o magnetisation, Bloch equations, relaxation times T1 and T2 o spin gymnastics and image contrast o magnets, gradients and radio-frequency coils o quantitative MRI o functional MRI, flow, diffusion, perfusion measurements

• Nuclear Medicine o principles of radio-tracer detection o scintigraphy o single photon emission computed tomography (SPECT) o positron emission tomography (PET)

• ultrasound (US) o sound generation and propagation in tissue o US imaging o Doppler US o therapeutic applications of US (Lithotrypsy)

• X-ray Imaging o properties and generation of X-rays o fluoroscopy o computed tomography o image reconstruction from projections

• role of medical imaging in o the detection of disease o in patient management

• therapy monitoring

Literature • Oppelt A: Imaging Systems for Medical Diagnostics



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• Dössel O: Bildgebende Verfahren in der Medizin: Von der Technik zur medizini-schen Anwendung



Workload (hours)



Usability M.Sc. Physics: “Elective Subjects” (SL), M.Sc. Applied Physics: “Applied Physics” (SL or PL) or “Elective Subjects” (SL)

Language English



63

5.14. Biophysics of Cardiac Function and Signals (5 ECTS)

Module no. 07LE33M-CARDI

Biophysics of cardiac function and signals 5 ECTS

Lecturer/s Dr. Gunnar Seemann, Prof. Dr. Peter Kohl (Faculty of Medicine, Institute for Experi-mental Cardiovascular Medicine)



Term The lecture is offered regularly in the winter semester.


The basic concept of this lecture is to examine a biological system, analyse it and define mathematical equations in order to describe the system. In this lecture, the heart is used as this system. The students learn the electrical and mechanical function of the heart and its modelling. Additionally, the bioelectrical signals that are generated in the human body are described and how these signals can be measured, interpreted and processed. The content is explained both on the biological level and based on mathe-matical modelling.

Course content • Cell membrane and ion channels • Cellular electrophysiology • Conduction of action potentials • Cardiac contraction and electromechanical interactions • Optogenetics in cardiac cells • Numerical field calculation in the human body • Measurement of bioelectrical signals • Electrocardiography • Imaging of bioelectrical sources • Biosignal processing

Literature • lecture slides


Basic interest in biology and computational modelling. Knowledge in Matlab or Python are beneficial


Workload (hours)




Language English



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5.15. Computational Neuroscience: Models of Neurons and Networks (7 ECTS)

Module no. 07LE33M-Neuro

Computational Neuroscience: Models of Neurons and Networks 7 ECTS

Lecturer/s Prof. Dr. Stefan Rotter (Faculty of Biology, Bernstein Center Freiburg)





The students have the competence to • link mathematical models with biological phenomena arising in systems neurosci-

ence both using theory and computer simulations; • understand the fundamental trade-off between biological detail and mathematical

abstraction, and evaluate its consequences; • explain the steps necessary to develop and validate models of a biological neuron

or a biological neuronal network; • appreciate and explain the gain in understanding biological mechanisms that arise

from the study of mathematical models of neuronal systems; • critically discuss the limits of mathematical modelling and numerical methods in

computational neuroscience.

Course content This lecture series covers important standard topics in computational neuroscience, focusing on dynamic networks of spiking neurons • Mathematical concepts and methods • Hodgkin-Huxley theory of the action potential • Stochastic theory of ionic channels • The integrate-and-fire neuron model • Stochastic point processes • Stochastic theory of synaptic integration • Stochastic theory of spike generation: The perfect integrator • Stochastic theory of spike generation: The leaky integrator • Conductance based neurons and networks • Correlated neuronal populations • Pulse packets and synfire chains • Random graphs and networks • Dynamics of spiking networks • Population dynamics of recurrent networks.

Literature • lecture slides • a bibliography and web-links to complementary reading for each course day will

be provided along with the slides of the lecture.


Familiarity with elementary calculus and linear algebra is assumed. Background in basic neurobiology is helpful, but not required.



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Final Exam Written exam (120 min), oral exam (60 min) or term paper (10 pages), in combination with course below.

Workload (hours)




Language English



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5.16. Computational Neuroscience: Simulation of Biological Neuronal Networks (5 ECTS)

Module no. 07LE33M-Neuro

Computational Neuroscience: Simulation of Biological Neuronal Networks 5 ECTS

Lecturer/s Prof. Dr. Stefan Rotter (Faculty of Biology, Bernstein Center Freiburg)





• link mathematical models with biological phenomena arising in systems neurosci-ence, both using theory and computer simulations;

• implement and simulate simple neuronal network models using modern tools and methods of scientific programming (based on Python and NEST);

• implement simple programs for data analysis and apply them to simulated data; • appreciate and explain the gain in understanding biological mechanisms that arise

from the study of mathematical models of neuronal systems and their simulation • critically discuss the limits of mathematical modelling and numerical methods in

computational neuroscience.

Course content This course covers the fundamentals of simulating networks of single-compartment spiking neuron models. We start from the concept of a point neuron and then introduce more complex topics such as phenomenological models of synaptic plasticity, connec-tivity patterns and network dynamics.

Literature • lecture slides • see also http://www.nest-initiative.org/ for some general information and an online

tutorial on the BNN simulator NEST


Basic knowledge in scientific computing with Python is absolutely required. Self-study is possible, see http://www.python.org/ for some general information and an online tu-torial on the programming language Python. Further documentation on the scientific libraries used in the course is also found online (see http://scipy.org/).

Final Exam Written exam (120 min), oral exam (60 min) or term paper (10 pages), in combination with course above.

Workload (hours)




Language English



67

5.17. Experimental Polymer Physics (9 ECTS)

Module no. 07LE33M-POL

Experimental Polymer Physics 9 ECTS

Lecturer/s Prof. Dr. Günter Reiter





Course content We can't imagine life and technology today without polymers, if you think of materials like PET bottles and PVC, nylon, teflon or rubber. Also in nature biopolymers are ubiq-uitous, e.g. DNA, proteins or cellulose. This lecture will give an introduction into the experimental and theoretical concepts in understanding and characterisation of poly-mer systems. Both, applied and material aspects will be discussed - like polymer flow, elastomers and crystalline polymers - as well as present topics of fundamental re-search, e.g. glass transition, dynamics in confined geometries and self-assembly. The lecture will deal with basic theoretical concepts and descriptive experiments. It will start with simple single chain phenomena and gradually develop more complex structures and dynamics of polymer solutions, melts and blends.

Literature • G. Strobl, The Physics of Polymers • Colby & Rubinstein, Polymer Physics


Experimental Physics I-IV (B.Sc. Physik), Thermodynamics


Workload (hours)



Usability M.Sc. Physics: “Advanced Physics 2” (PL), “Advanced Physics 3” (SL), “Elective Sub-jects” (SL), M.Sc. Applied Physics: “Advanced Experimental Physics” (PL), “Applied Physics” (PL or SL) or “Elective Subjects” (SL)

Language English



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5.18. Physical Processes of Self-Assembly and Pattern Formation (7 ECTS)

Module no. 07LE33M-SELFAS

Physical Processes of Self-Assembly and Pattern Formation 7 ECTS

Lecturer/s Prof. Dr. Günter Reiter





Students will learn how structural organization, i.e., the increase in internal order of a system, can lead to regular patterns on scales ranging from molecular to the macro-scopic sizes. They will understand the physics of how molecules or objects put them-selves together without guidance or management from an outside source.

Course content Goal: Questions about how organization and order in various systems arises have been raised since ancient times. Self‐assembling processes are common throughout nature and technology. The ability of molecules and objects to self‐assemble into supra‐mo-lecular arrangements is an important issue in nanotechnology. The limited number of forms and shapes we identify in the objects around us represent only a small sub-set of those theoretically possible. So why don't we see more variety? To be able answering such a question we have to learn more about the physical processes responsible for self-organization and self-assembly. Preliminary program: “Physical laws for making compromises” Self-assembly is governed by (intermolecular) interactions between pre‐existing parts or disordered components of a system. The final (desired) structure is 'encoded' in the shape and properties of the basic building blocks. In this course, we will discuss general rules about growth and evolution of structures and patterns as well as methods that predict changes in organization due to changes made to the underlying components and/or the environment.

Literature • Yoon S. LEE, Self-Assembly and Nanotechnology:A Force Balance Approach, Wiley 2008

• Robert KELSALL, Ian W. HAMLEY, Mark GEOGHEGAN, Nanoscale Science and Technology, Wiley, 2005

• Richard A.L. JONES, Soft Machines: Nanotechnology and Life, Oxford University Press, USA 2008

• Philip BALL, Shapes, Flow, Branches. Nature's Patterns: A Tapestry in Three Parts, Oxford University Press, USA

• J.N. ISRAELACHVILI, Intermolecular and Surface Forces, Third Edition, Else-vier, 2011

• Continuative and supplementary references will be given during the lecture.



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Experimentalphysik IV (Condensed Matter)


Workload (hours)




Language English



70

5.19. Fundamentals of Semiconductors & Optoelectronics (5 ECTS)

Module no. 07LE33M- HL

Fundamentals of Semiconductors & Optoelectronics 5 ECTS

Lecturer/s apl. Prof. Dr. Joachim Wagner (Fraunhofer IAF), Prof. Andreas Bett (Fraunhofer ISE)





• Students become familiar with fundamental concepts of semiconductor physics as well as techniques for the fabrication of bulk semiconductor materials and epitaxial semiconductor layers; furthermore, they gain knowledge in experimental tech-niques for the characterization of semiconductors as well as for determining band structure parameters.

• Students become also familiar with the working principle and different variants of key optoelectronic devices.

Course content • Inorganic crystalline semiconductor materials (such as Si and GaAs) • Fabrication of bulk semiconductor crystals and epitaxial layers • Electronic band structure, tight-binding vs. nearly free electron approach • Effective mass of electrons and holes, n- and p-type doping • Density of states, statistics of electrons and holes • Electrical transport by electrons and holes, electric fields and currents • Quantization effects in semiconductors, quantum films and superlattices • p-n-junction, photodiode, light emitting diode (LED), diode laser

Literature • H. Ibach, H. Lüth, „Festkörperphysik" (Springer, 2009) • K. Seeger, „Semiconductor Physics“ (Springer, 2004) • P. Yu, M. Cardona, „Fundamentals of Semiconductors“ (Springer, 2010)


Solid-state physics and theoretical physics at the level of a BSc in Physics

Final Exam Oral exam (30 min)

Workload (hours)







71

5.20. Semiconductor Devices (5 ECTS)

Module no. 07LE33M- HLBAU

Semiconductor Devices 5 ECTS

Lecturer/s apl. Prof. Dr. Harald Schneider (Helmholtz-Zentrum Dresden-Rossendorf HZDR)



Term The lecture is offered in the summer semester as a block course during the Pentecost break (May/June)


Course content • Transport phenomena • Metal-semiconductor-contact, Schottky-Diode • p-n junction: diode rectifier, photodiode, LED, laserdiode, solar cell • Bipolar transistors, HBT • Field effect-transistors: JFET, MESFET, HEMT, MOSFET, FGFET • Quantum structure-elements: RTD, QWIP, QCL, ICL

Literature • S.M. Sze and K.K. Ng, Physics of Semiconductor Devices, Wiley, 2006 • S.M. Sze, Semiconductor Devices, Wiley, 2001


Experimentalphysik IV (Solid state physics), lecture „Fundamentals of Semiconductors & Optoelectronics” (apl. Prof. J. Wagner)


Workload (hours)







72

5.21. Theory and Modeling of Materials (5 ECTS)

Module no. 07LE33M- MODMAT

Theory and Modeling of Materials 5 ECTS

Lecturer/s apl. Prof. Dr. Christian Elsässer (Fraunhofer IWM)



Term Courses of the lecture series are offered regularly in alternating order.


• Students become able to develop and apply theoretical models to investigate prac-tical problems of the physics of materials

• Students become familiar with theoretical condensed-matter physics and compu-tational modeling and simulation of materials

Course content The series of one- or two-semester elective-subject lectures introduces theoretical models and computational methods of solid-state physics for the description of many-electron systems, by means of which cohesion and structure, physical, chemical, or mechanical properties of perfect crystals and real materials can be understood qualita-tively and calculated quantitatively on a microscopic fundament. The lecture series comprises courses on, e.g., these topics: • Electronic-structure theory of condensed matter I + II • Superconductivity I (phenomenology) + II (microscopic theory) • Theoretical models for magnetic properties of materials • Theory of atomistic and electronic structures at interfaces in crystals • etc.

The content of each course will be announced for each semester.

Literature recommended literature will be announced in each lecture


Theoretical physics and solid-state physics on the level of a BSc in Physics


Workload (hours)







73

5.22. Quantum Transport (7 ECTS)

Module no. 07LE33M- QTRANS

Quantum Transport 7 ECTS

Lecturer/s PD Dr. Michael Walter, PD Dr. Thomas Wellens



Term The lecture is offered irregularly in the summer semester.


• Students become familiar with advanced theoretical tools relevant for quantum transport theory (Green functions, scattering theory, diagrammatic methods for performing disorder average, Landau-Büttiker formalism)

• Students understand how quantum effects modify the transport behaviour in vari-ous physical systems

Course content How to describe transport of a particle from one point in space to another one is a fundamental problem in theoretical physics, which is at the same time highly relevant for many technological applications, for example in electronics (transport of electrons) or solar cells (separation of positive and negative charge carriers generated by light). On microscopic scales, quantum properties -- such as the wave nature of a quantum particle, or the quantization of energy levels -- become relevant and make quantum transport different from classical transport based on Newton's equations. In this lecture, we will approach the topic of quantum transport from different perspectives, with focus on (i) transport of quantum particles (or waves) in disordered structures which are de-scribed in a statistical way, and (ii) the explicit description of transport in an electronic device at the atomic scale, with the single molecule transistor as prominent example, which is likely to be the basis of future electronics.

Literature • E. Akkermans and G. Montambaux, Mesoscopic Physics of electrons and photons (Cambridge University Press, Cambridge, 2007)

• P. Sheng, Introduction to Wave Scattering, Localization, and Mesoscopic Phenom-ena (Academic Press, New York, 1995)

• S. Datta, Quantum Transport: Atom to Transistor (Cambridge, 2005).

Previous knowledge Basic quantum mechanics


Workload (hours)




Language English



74

5.23. Low Temperature Physics (9 ECTS)

Module no. 07LE33M- LTPHYS

Low Temperature Physics 9 ECTS

Lecturer/s Prof. Dr. Frank Stienkemeier





• The lecture Low Temperature Physics provides an introduction to the physical prin-ciples as well as the experimental techniques for working at low temperatures and reaching extreme low temperature conditions.

• Students will be familiar with material properties at low temperatures. • Students will know how low temperatures are generated, how cryostats are de-

signed, and what materials are used. • Students will learn modern scientific work at low as well as ultra-low temperatures

Course content • Temperature-dependent material properties (Phase diagrams and physical states, thermal expansion, friction, viscosity, thermal conductivity, electrical con-ductivity)

• Superfluidity • Matrix and helium droplet isolation techniques • Superconductivity • Generation of low temperatures (refrigerators, Joule-Thompson effect, cryo-

coolers) • Measurements at low temperature conditions (temperature, pressure, levels of

liquids, magnetic measurements, acoustic measurements, etc.) • Cryostats (thermal insulation, materials, containers and transfer lines, etc.) • Cold dilute samples (cold molecular beams, trapped molecules and trapped

ions) • Ultra-cold temperatures

Literature • Enss, Hunklinger, Tieftemperaturphysik, Springer (2000) • Frank Pobell, Matter and Methods at Low Temperatures, Springer (1996) • J.G. Weisend II, Handbook of Cryogenic Engineering, Taylor & Francis (1998)


Experimental Physics I-IV Quantum Mechanics


Workload (hours)





75

Usability M.Sc. Physics: “Advanced Physics 2” (PL), “Advanced Physics 3” (SL), “Elective Sub-jects” (SL), M.Sc. Applied Physics: “Advanced Experimental Physics” (PL), “Applied Physics” (PL or SL) or “Elective Subjects” (SL)

Language English



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5.24. Statistics and Numerics (7 ECTS)

Module no. 07LE33M-STATNUM

Statistics and Numerics 7 ECTS

Lecturer/s Prof. Dr. Jens Timmer





• Students are familiar with the basic concepts of statistical reasoning. • Students are able to mathematically formulate statistical and numerical problems. • Students can implement computer programs to solve statistical and numerical

problems.

Course content • Random variables • Parameter estimation • Test theory • Solution of systems of linear equations • Optimization • Non-linear modeling • Kernel estimator • Integration of ordinary, partial and stochastic differential equations • Spectral analysis • Markov Chain Monte Carlo procedures

Literature • Press et al. Numerical Recipes, Cambridge University Press


Basics of Analysis and Linear Algebra


Workload (hours)







77

5.25. Computational Physics: Density Functional Theory (7 ECTS)

Module no. 07LE33M-DFT

Computational Physics: 7 ECTS Density Functional Theory

Lecturer/s Prof. Dr. Michael Moseler





• Students are familiar with electronic structure calculations. • Students are familiar with the basic Hamiltonian of the electronic structure prob-

lem and electronic many-body wave function. • Students know the Hartree-Fock equations and post Hartree-Fock methods –

such as Møller-Plesset and Configurational Interaction. • Students are familiar with the Hohenberg-Kohn-theorem, the Kohn-Sham-equa-

tions, the concept of an exchange-correlation potential and the various local ap-proximations to it.

• Student arefamiliar with time-dependent DFT and know the Runge-Gross-theo-rem and the time-dependent Kohn-Sham-equations.

Course content Density functional theory (DFT) has become one of the most important tools for the numerical solution of the electronic many-body Schrödinger equation. It is currently used by many material scientists to study the properties complex systems containing up to several thousand atoms and electrons. This lecture introduces the theoretical foundations of DFT within the Hohenberg-Kohn-Sham frame work. It also touches nu-merical questions in an accompanying hands-on course. Numerical exercises will cover the electronic structure of atoms and nanoparticles.

Literature Lecture script: Electronic structure of matter


Basic knowledge in many-body quantum mechanics


Workload (hours)




Language English



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6. Example study plans for optional specialisation Within their Master studies, students may consolidate their knowledge in a particular field of phys-ics by choosing their courses in the modules Advanced Physics, Elective Subjects and Term Paper accordingly, as well as performing their research phase (Research Traineeship and Master Thesis) in this field. In the following example, study plans are recommended for different areas of special-isation. Example Study Plan for consolidation in Experimental Particle Physics:

FS

1 Advanced Quantum Mechanics 10 CP

Advanced Particle Physics 9 CP

Term Paper in Particle Physics 6 CP

Master Laboratory 8 CP

2 Quantum Field Theory 9 CP

Hadron Collider Physics 9 CP

Detectors 9 CP

3 Research Traineeship in Experimental Particle Physics 30 CP

4 Master Thesis in Experimental Particle Physics (Thesis and Presentation) 30 CP

Example Study Plan for consolidation in Theoretical Particle Physics:

FS


General Relativity 9 CP

Term Paper in Particle Physics 6 CP

Master Laboratory 8 CP

2 Quantum Field Theory 9 CP

Hadron Collider Physics 9 CP

Quantum Chromodynamics 9 CP

3 Research Traineeship in Theoretical Particle Physics 30 CP

4 Master Thesis in Theoretical Particle Physics (Thesis and Presentation) 30 CP



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Example Study Plan for consolidation in Atomic, Molecular and Optical Physics:

FS


Advanced Atomic and Molecular Physics 9 CP

Term Paper in Atomic and Mo-lecular Physics 6 CP

Master La-boratory 8 CP

2 Advanced Optics and Lasers 9 CP

suggested* theory lectures 9 CP

suggested** experimental lectures 9 CP

3 Research Traineeship in Experimental Atomic and Molecular Physics 30 CP

4 Master Thesis in Experimental Atomic and Molecular Physics (Thesis and Presentation) 30 CP

* Choose for example: Classical Complex Systems Theoretical Quantum Optics Complex Quantum Systems Theoretical Condensed Matter Physics

** Choose for example: Condensed Matter I: Solid State Physics Condensed Matter II: Interfaces and Nanostructures

Example Study Plan for consolidation in Condensed Matter Physics:

FS


Condensed Matter I: Solid State Physics 9 CP

Term Paper in Condensed Matter Physics 6 CP

Master La-boratory 8 CP

2 Theoretical Condensed Matter Physics 9 CP

Condensed Matter II: Interfaces and Nanostructures 9 CP

Complex Quantum Sys-tems 9 CP

3 Research Traineeship in Condensed Matter Physics 30 CP

4 Master Thesis in Condensed Matter Physics (Thesis and Presentation) 30 CP

master-of-science (m.sc.) physics - uni-freiburg.de

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